Solutions to HW4

 

Economics 172

Spring 2005

 

Homework 4

Due Wednesday Feb 16

 

 Review questions

 

4.2

4.9

4.10

4.17

4.20

4.27

 

4.2  If the price of one unit of college education rises and the price of all other goods (the composite good) falls, the consumer could (but does not always have to) be on the same indifference curve.   The old budget line was AZ and the new one is KK’.   If the consumer on the same indifference curve, she will never buy the same market basket as she did before (at point E).

The new marginal rate of substitution at point E’ is higher than it used to be at point E, since the consumer will change her optimal consumption bundle to reflect the new relative prices (that is the slope of the new budget line, which is Ped/Pog).  So the consumer will always buy more other goods and less education.

 

 

 

 

 

 

 

 

4.9 a. This is a good question to show the interactions between micro and statistics (actually econometrics).   The demand equation is

 Qi = a + bPi + cIi + dPPAYi + ei .   And you are given that b = -230.0 c = -0.01  d = -99.5

The average monthly per capita income is $6,677.40 and the number of subscribers is 5,370.

 

The income elasticity of demand  for basic cable service is (% Ch Qd/% Ch Income) which is (ChQd/ChInc)(I/Q)

 

Ch Qd/Ch Inc is c which is  -.01  so the income elasticity is (-.01)(6677/5370) = -.012   This means that cable is an inferior good (since its sign is negative).  However, the actual number is very small (that is, close to zero) and we would have to know the statistical significance of the coefficient in order to determine whether it is valid.

 

b.  The cross price elasticity of demand for basic service with respect to the pay tier price:

 

%Ch Qd of cable / % Ch Pay Tier Price          Evaluated at the average values:

 

(Ch Qd/Ch Pay Tier price) (Pay Tier Price/Qd Basic Cable)   The Ch Qd cable/Ch Pay tier price is d which is -99.5 and Pay Tier Price / Qd Basic cable is $13/5370 .   So -99.5 (13/5370) = -0.24   Since the cross price elasticity is negative, the two products are complements.

 

c.  The income elasticity of demand for basic service evaluated at the income and quantity data for system 3:

 

 (% Ch Qd/% Ch Income) which is (ChQd/ChInc)(I/Q) but this time we substitute in the values for system 3 for I/Q or 8900/3900

So the elasticity is (-.01)(8900/3900) = -0.023.  This is also a negative number so the income elasticity shows that it is an inferior good for system 3.

 

4.10  If butter and butcher knives are both inferior, then the only other good Lorena consumes must be a normal good.  Her income goes up and she’s spending more on butter knives and butcher knives.  She must spend more on steak knives.

 

4.17  Left and right shoes are perfect complements.  If the price of right shoes goes up, there is no substitution effect.  Even though left shoes are now cheaper, you must use left and right shoes together so you can’t substitute away from right shoes and buy more left shoes.   The budget line shifts from AZ to AZ’  To analyze the substitution effect, we push budget line AZ’ outward until it is tangent to the original indifference curve.  There is no substitution effect, since we stay at point E

There is only an income effect, which brings the consumer from R1 right shoes to something less (an indifference curve tangent to AZ’).

 

 

 

 

 

 

 

 

4.20   As we discussed in class, this problem is known as the water-diamond paradox. The solution to the paradox is to distinguish between total value and marginal value. Because the supply of water is large relative to demand, while the supply of diamonds is low relative to demand, the market price for diamonds is higher than the market price for water. The market for water is in the graph on the left below and the market for diamonds in the graph on the right. The large demand for water intersects the  large suply of water, generating a low price, C, while the demand and supply for diamonds are both much less than those for water, yet the price is high, F. These prices measure the marginal value for water and diamonds respectively. But, the total value for water, which is the

area ABW OW is much larger than the total value for diamonds, which is the area    DED OW. Further, consumer surplus is much greater for water than diamonds—area ABC versus area DEF.

 

 

 

4.27  The answer is uncertain.  The income effect can be greater, less than, or equal to the substitution effect.  It depends on how much hamburger consumption falls in the wake of a price increase. What is known for sure, however, is that hamburger is not sufficiently an inferior good to the consumer so that the positive income effect associated with the price decrease ends up outweighing the negative substitution effect (if the latter were indeed the case, consumption would rise in the wake of the price increase).